Two Statistical Methods 0 Introduction Statistical methods have evolved over a period to time to address specific needs of industries, governments and society at large. Statistical studies follow either the experimental or the observational path. Whatever be the approach or study that is taken up, the analysis of the data is done using any of the number of statistical methods that are available. Each one of them is used to reach specific targets. For our current consideration, we have taken up, the chi-square distribution and the Analysis of Variance (ANOVA)1.

2.0 The chi-square Distribution

A chi-square distribution stems out of the concept that under the assumption that null hypothesis is true, any calculated inferences from a dataset would follow a distribution matching the chi-square distribution.

This distribution is a theoretical method used normally to have the goodness of fit of an observed statistic to a theoretical model and the degrees of freedom that it is calculated to. The chi-square is used to test both of these parameters. Most often this is used in specifically to address the issues relating to proportion of population. Two chi-square tests are comfortably used. one, test for goodness of fit and two, test for independence2.

3.0 Analysis of Variance

Analysis of Variance provides the methodology to analyses a dependent variable and the effect of other interval independent variables on the values of the dependent variable. ANOVA (Analysis of Variance) may be One-way ANOVA when the effect of one independent variable is measured. However, effects of multiple interval independent variables can be measured. This helps in substantiating the ‘main effects’ and the ‘interaction effects’3.

Main effects bring out the direct variation in the dependent variable due to every single independent variable. Whereas, the interact effect brings out the combined effect of the independent variables on the dependent variable. This is normally analyzed in various combinations. Two independent variables and their effects. then three of them and various combinations of them. in this manner, a complete analysis can be carried out to bring out the effects.

4.0 Conclusion

The methods adopted help in fiting the right curve or distribution, thereby helping in analyzing the dataset more thoroughly and effectively.

Bibliography

1. Wikipedia, Statistical methods, available at http://en.wikipedia.org/wiki/Statistical_methods

2. Wikipedia, chi-square Distribution, available at http://en.wikipedia.org/wiki/Chi-square

3. Statistics Solutions, Analysis of Variance, available at http://www.statisticssolutions.com/ANOVA.htm

4. SixSigma First, Analysis of Variance, available at http://www.sixsigmafirst.com/anova.htm

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